Geometric quantization and internal symmetry

Mathematics

Scientific paper

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Electromagnetic Radiation, Field Theory (Physics), Gravitational Fields, Hadrons, Quantum Theory, Eigenvalues, Geometry, Neutrinos, Operators (Mathematics), Polynomials, Symmetry, Tensors

Scientific paper

It is noted that the U(3) group of generalized duality rotations of the trace-free energy-momentum tensor appears as gauge symmetries in a geometric theory of quantization. This paper shows how various interactions break this symmetry in a manner analogous to the observed breaking of internal symmetry by using known results for different kinds of classical matter and the types of their energy-momentum tensors. Consideration is given to 'pure matter', 'pure fluid', electromagnetic radiation, and a neutrino field. The results obtained are found to resemble hadron physics, with hadrons interpreted as microscopic pure fluids, and to suggest that quantum field theory should be approached from an a priori generally covariant viewpoint with momentum vectors replaced by energy-momentum tensors.

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